Prior to beginning work on this discussion forum, read Section 8-4 of the Business Analytics: Data Analysis and Decision Making (8th edition) textbook. Also, review the Simulatio

Prior to beginning work on this discussion forum, read Section 8-4 of the Business Analytics: Data Analysis and Decision Making (8th edition) textbook. Also, review the Simulation interactive. Apex Sports is thinking about entering the golf ball market. The company will make a profit if its market share is more than 15%. A market survey indicates that 128 of 758 golf ball purchasers will buy an Apex Sports golf ball. In your initial post, answer the following questions: Is the market survey alone enough evidence to persuade Apex Sports to enter the golf ball market? How would you use hypothesis testing to help you make your decision if you were Apex Sports management and you required 90% confidence in your market research results? Does hypothesis testing support or not support entering the golf ball market? Show all your work. Besides the market survey results, what other considerations might enter your decision on whether to enter the golf ball market? If Apex Sports decides to enter the golf ball market, what are their probabilities for success? You do need to perform a hypothesis test for this assignment in order to reach a definitive conclusion. As stated in the introductory work, you also need to show detailed steps in your computations. It is best that you perform all your work and include all required computations in an Excel file and attach it to your post, the latter which explains in words the results of your hypothesis test. See my tutorial below for the steps you need to take and computations to perform in order to satisfactorily complete this assignment. We are told that 128 of 758 golf ball purchasers will buy an Apex Sports golf ball. How does this proportion compare to the statement that “The company will make a profit if its market share is more than 15%”? Since we are dealing with a proportion, we need to think about a hypothesis test for a population proportion. Here are the steps for the hypothesis test. Express both the null and alternative hypotheses. Recall that the null hypothesis is generally the currently accepted value (section 9-2a), which is explicitly stated in the statement of the problem. The alternative hypothesis is expressed as an inequality (larger-than, less-than, or not-equal). Think about the statement “The company will make a profit if its market share is more than 15%”. Is this an “at least” statement, “at most” statement, or neither? Based on your response to this question, you will have an idea how to express the alternative hypothesis. Compute the test statistic. In a hypothesis test for proportion (section 9-4a), the test statistic is given by equation 9.2: z-score = (p_hat – p0) / sqrt[ p0 (1 – p0) /n ] We have all the information needed to compute the above expression. Note that as stated in the textbook, the assumption is that the distribution of sample proportions is approximately normal. Having computed the z-score, we are in a position to determine the p-value (step 4 below). First, we need to determine whether we are dealing with a one-tailed test or a two-tailed test (section 9-2b). To do so, we have to see whether the alternative hypothesis is concerned with a single direction (less-than or greater-than the value of the parameter in the null hypothesis), or in either of two directions (not-equal to value of the parameter in the null hypothesis). This step is determined by how we stated the alternative hypothesis in step 1. We will use the p-value method (section 9-2e) to determine the statistical significance (section 9-2d) of the empirical evidence we have obtained, the latter being that “128 of 758 golf ball purchasers will buy an Apex Sports golf ball”. The p-value will give us a quantitative value to decide whether this evidence is statistically significant, that is whether there is good reason to believe the market share is more than 15%. We can interpret the statement that Apex Sports management “required 90% confidence” equivalent to the requirement that they are willing to accept a Type I error of 10%, that is a significance level of 0.1. We will compare the p-value to this value of significance level in order to arrive at the conclusion of the hypothesis test. The smaller the p-value, the more evidence we have to reject the null hypothesis in favor of the alternative hypothesis. The p-value simply expresses numerically the probability of arriving at, say “128 of 758 golf ball purchasers”, purely by chance. Hence, the lower this probability, there is less reason to believe that we got “128 of 758 golf ball purchasers” just by chance, indicating that the evidence is statistically significant in favor of the alternative hypothesis. Figure 9-2 shows various scenarios for interpreting a p-value. First, a clarification about terminology: In most statistics textbooks the proportion between two quantities is expressed by the variable p, which may cause confusion with the other widely used variable p-value. The p in p-value stands for probability, not proportion, so be careful to keep in mind the distinction between variables p (proportion) and p-value. Continuing with our analysis, since we are assuming that the distribution of sample proportions is approximately normal, we can easily compute the p-value using Excel’s NORMSDIST function, where its argument is the value of the z-score computed in step 2. As explained in section 9-2 there are two types of hypothesis test: one-tailed and two-tailed. The present problem is a case of a one-tailed test. Additionally, one-tailed tests can be either right-tailed or left-tailed. In right-tailed tests the null and alternative hypotheses are expressed as H0: p ≤ hypothesized-value and H1: p > hypothesized-value. This is the case in example 9.1, section 9-3. On the other hand in the left-tailed tests the directions are reversed, that is we have H0: p ≥ hypothesized-value and H1: p < hypothesized-value. It is up to you to decide whether to go with a right-tailed or a left-tailed test. However we have to be a bit careful, since if our alternative hypothesis is expressed as less-than (left-tailed test) then p-value = NORMSDIST(z-score), whereas if the alternative hypothesis is expressed as more-than (right-tailed test) then p-value = 1 – NORMSDIST(z-score). I have attached the solution to problem 10 from chapter 9, which is very similar to this problem